Comment: The correct starting point for counting

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The correct starting point for counting

is "1." We count with "natural numbers," another term for which is, actually, "counting numbers." These consist of the set of positive integers {1, 2, 3,...}. Possibly they are called "natural" numbers because for eons we've been using something organic, our fingers, to count on. And you'd never be counting "zero" items or whatever. If there were zero items, there would be nothing there for you to count.

In fact, zero wasn't used as a number until fairly recently in the scheme of things: "The concept of zero as a number and not merely a symbol for separation is attributed to India, where, by the 9th century AD, practical calculations were carried out using zero, which was treated like any other number, even in case of division."

Now, we don't have nine fingers, but ten. But as the guy pointed out (it's integral (no pun intended) to the way he is looking at numbers here), the 10 is comprised of 1+0=1. Maybe we don't think of it this way, but zero is used in two ways, as a place holder and as a number itself (to mean "nothing"). In the number 10 (vs., say, 100 or 1), the zero is used to position the 1 to reflect its value, i.e., to differentiate 1 group of ten from 1 group of a hundred or 1 one).

I'm pointing out that counting numbers begin with "1" so you don't write off the guy on that basis alone.

I, too, am fascinated by pi. Also by Archimedes (287-212 B.C.), who must have had the patience of a saint! "By inscribing and circumscribing a 96-sided regular polygon in and about a circle he computed that pi is between 3 1/7 and 3 10/71." (Source: The Historical Roots of Elementary Mathematics, by Lucas N.H.Bun, Phillip S. Jones, and Jack D. Bedient)

Now I could imagine myself drawing a square both inside and outside of a circle with some precision. But here's a chart of regular polygons (regular polygons being multi-sided figures with equal sides and angles):

A dodecagon, which is only a 12-sided figure, is already beginning to look circular, what I have to imagine is difficult to draw with just a straightedge and compass to get those 12 sides and angles all the same. Imagine Archimedes drawing a 92-sided figure with all the sides and angles being equal!

So based on the areas of his "little" inscribed dodecagon and "big" circumscribed dodecagon, and knowing that the area of the circle would be between those two values, Archimedes was able to figure out that (here, going out to just five places) the value of pi (3.14159) was between 3 1/7 (or 3.14286) and 3 10/71 (or 3.14085).

Well, there's a lot about mathematics that fascinates me.

When we try to pick out anything by itself, we find it hitched to everything else in the Universe.
~ John Muir